# General Log-Linear (GLL)-Weibull Model

 General Log-Linear (GLL)-Weibull Model

This example validates the results for the GLL life-stress relationship with a Weibull distribution in ALTA standard folios.

Reference Case

The data set is from Example 7.14 on page 297 in book Life Cycle Reliability Engineering by Dr. Guangbin Yang, John Wiley & Sons, 2007.

Data

The following table shows the data.

State F/S Time to State (Hr) Temperature (°C) Group ID
F 1138 100 1
F 1944 100 1
F 2764 100 1
F 2846 100 1
F 3246 100 1
F 3803 100 1
F 5046 100 1
F 5139 100 1
S 5500 100 1
S 5500 100 1
S 5500 100 1
S 5500 100 1
F 1121 120 2
F 1572 120 2
F 2329 120 2
F 2573 120 2
F 2702 120 2
F 3702 120 2
F 4277 120 2
S 4500 120 2
F 420 150 3
F 650 150 3
F 703 150 3
F 838 150 3
F 1086 150 3
F 1125 150 3
F 1387 150 3
F 1673 150 3
F 1896 150 3
F 2037 150 3

Result

The model used in the book is:

$\,\!ln\left ( \eta \right )=\alpha _{0}+\alpha _{1}\frac{1}{T}$

The book has the following results:

• The model parameters are: $\,\!\alpha _{0}=-3.156$ , $\,\!\alpha _{1}=4390$ and $\,\!\beta =2.27$.

• The variance of each parameter is: $\,\!Var\left ( \alpha _{0} \right )=3.08$ , $\,\!Var\left ( \alpha _{1} \right )=484819.5$ and $\,\!Var\left ( \beta\right )=0.1396$ .

• The two-sided 90% confidence intervals for the model parameters are: $\,\!\left [ \alpha _{0,L},\alpha _{0,U} \right ]=\left [ -6.044, -0.269 \right ]$ , $\,\!\left [ \alpha _{1,L},\alpha _{1,U} \right ]=\left [ 3244.8, 5535.3 \right ]$ and $\,\!\left [ \beta _{1,L},\beta _{1,U} \right ]=\left [ 1.73, 2.97 \right ]$ .

• The estimated B10 life at temperature of 35°C is 24,286 hours. The two-sided 90% confidence interval is [10371, 56867].

• The estimated reliability at 35°C and 10,000 hours is $\,\!R\left ( 10000 \right )=0.9860$ . The two-sided 90% confidence interval is [0.892, 0.998].

Results in ALTA

In ALTA, the GLL model with Weibull distribution is used. Since temperature is the stress, the reciprocal transform is used. The results are:

• The model parameters are:

• The variances of the parameters are:

• The two-sided 90% confidence intervals for the model parameters are:

• The estimated B10 life and its two-sided 90% confidence intervals are:

• The estimated reliability with its two-sided 90% confidence interval at 35°C and 10,000 hours are: